opsmath1.weebly.comopsmath1.weebly.com/uploads/1/5/3/9/15394680/ced.3_… · Web viewEach manicure takes 30 minutes, and each pedicure takes ... Andre is paid $12 per hour at his

CED.3 [1815694]StudentClassDate

1.The graphs of y = –2x + 5, y = 2, and are shown below.

Which lettered point on the grid satisfies the system of inequalities?

A. A

B. B

C. C

D. D

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2. Lars needs to purchase at least 35 party decorations. The Party Palace charges $0.50 per decorative streamer and $0.25 per balloon, including tax. Which combination of streamers and balloons can Lars purchase with $11.50 at the Party Palace?

A. 19 streamers and 16 balloons

B. 12 streamers and 22 balloons

C. 11 streamers and 25 balloons

D. 9 streamers and 27 balloons

3. Kim works at a nail salon doing manicures and pedicures.

Each manicure takes 30 minutes, and each pedicure takes 45 minutes.

She has at least 3 manicures a day. She earns a profit of $10 per manicure and $20 per

pedicure. She can only work 8 hours per day.

To maximize her profit, how many more pedicures than manicures should Kim do?

A. 7

B. 6

C. 4

D. 2

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4. Harry needs to buy hamburgers and hot dogs for a picnic. He has only $41.00 to spend and must buy at least 98 hamburgers or hot dogs. A store charges $.50 per hamburger and $0.25 per hot dog. Which of the following is a possible way Harry might buy the hamburgers and hot dogs?

A. 78 hamburgers and 20 hot dogs

B. 69 hamburgers and 28 hot dogs

C. 66 hamburgers and 33 hot dogs

D. 64 hamburgers and 35 hot dogs

5. Grace wants to buy some new clothes, but she cannot afford more than $75 before the sales tax is added. The blouses she wants are priced $17 each and the pants she wants are priced $25 each. Which inequality could be used to determine b, the number of blouses, and p, the number of pants Grace can afford?

A.

B.

C.

D.

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6. Kiyoshi is replacing some of the flooring in his house. He will need 200 square feet of hardwood flooring and 350 square feet of carpet. He would like to determine the possible prices per square foot for both types of flooring, keeping the cost to no more than $2,000. Which inequality describes this situation?

x = price of hardwood flooring per square footy = price of carpeting per square foot

A.

B.

C.

D.

7. Zach wants to earn money by selling baked goods. He wants to sell at least 15 dozen baked goods each week. He can make at most 10 dozen cupcakes and at most 12 dozen cookies each week. Which inequalities best model this situation?

A.

B.

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C.

D.

8. Monika is in charge of ordering pens for an upcoming convention. Pens come in boxes of 6 and boxes of 8 and Monika needs at least 720 pens. Which inequality describes this situation?

x = number of boxes of 6 pensy = number of boxes of 8 pens

A.

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B.

C.

D.

9. Tom wants to compare two different plans for gym membership. The first plan charges a sign-up fee of $25.00, then $5.00 for every visit. The second plan charges $100.00 per month with no sign-up fee. Tom creates a graph to find the solution to this pair of equations.

Which statement most accurately compares the two plans?

A. If Tom plans to go to the gym 14 or fewer times during the month, he will pay less with the second plan.

B. If Tom plans to go to the gym 14 or fewer times during the month, he will pay

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less with the first plan.

C. If Tom plans to go to the gym 14 or more times during the month, he will pay less with the second plan.

D. If Tom plans to go to the gym 14 or more times during the month, he will pay less with the first plan.

10. A school is purchasing kneepads and headbands for the gym. The school budget this year allows the staff members to spend no more than $1,500, and they want to orderat least 250 items. They must buy at least as many kneepads as headbands. Each kneepad costs $5 and each headband costs $8. Which of these combinations of number of kneepads, x, and number of headbands, y, will satisfy the given conditions?

/files/assess_files/4b5ac7d3-faac-4fc7-8ca4-a25c867d584d/formula_sheets/FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf

FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf

A.

B.

C.

D.

11.Cashews and peanuts are combined to make a nut mixture. At least of the mixture, by weight, is cashews, and the total weight of the mixture cannot exceed 48

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ounces. Which system of inequalities models this situation, where c represents the number of ounces of cashews and p represents the number of ounces of peanuts?

A.

B.

C.

D.

12. Trevor earns $12 per hour and Brian earns $10 per hour. Which of the following situations can be modeled by the inequality below?

A. If Trevor and Brian each work x hours, Trevor’s earnings are at least $30 more than Brian’s earnings.

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B. If Trevor and Brian each work x hours, Trevor’s earnings are at most $30 more than Brian’s earnings.

C. If Trevor works x – 30 hours and Brian works x hours, Trevor’s earnings are greater than or equal to Brian’s earnings.

D. If Trevor works x – 30 hours and Brian works x hours, Brian’s earnings are greater than or equal to Trevor’s earnings.

13. The Randolph family has a 100-acre farm where the family raises two crops, x and y. The Randolphs take part in a government grant program which requires them to plant at least 20 acres of each crop.

It costs the Randolphs $20 per acre to raise crop x and $40 per acre to raise crop y. The family has $2,600 to cover costs. This year, the profit from selling crop x is $25 per acre and the profit from selling crop y is $60 per acre.

The Randolphs want to calculate how many acres of each crop they should plant in order to maximize their profit. On an xy-coordinate graph, where the x and y-values of a point represent the number of acres of each crop planted, find:

the equations for the constraints of the feasable region, and the coordinates that indicate the maximum profit.

/files/assess_files/7d1529d6-b76c-4d10-94de-ed635e267e55/formula_sheets/FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf


A.

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B.

C.

D.

14. A college entrance exam has a verbal section and a math section. A student can score a maximum of 800 points in each. To qualify, a student has to score at least 600 points in math and a minimum total of 1100 points. Which ordered pair represents a combination of math scores, x, and verbal scores, y, of a student who qualifies?

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A.

B.

C.

D.

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15. Andre is paid $12 per hour at his caddying job and $9.50 per hour working at a local fast food restaurant. He would like to keep both jobs and earn at least $275.00 a week, but he can work no more than 25 hours. If x represents the number of hours Andre works at his caddying job and y represents the number of hours he works at the restaurant, which system models this scenario?

A.

B.

C.

D.

16. Which of the following situations can be modeled by the equation below?

A. The cost of x – 24 CDs at $8 each equals the cost of x CDs at $5 each.

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B. The cost of x + 24 CDs at $8 each equals the cost of x CDs at $5 each.

C. The cost of x CDs at $8 each is $24 less than the cost of x CDs at $5 each.

D. The cost of x CDs at $8 each is $24 more than the cost of x CDs at $5 each.

17. Tyler wrote an inequality to represent the x and y values given in the table.

x y

1 1 2 –1–2 2–3 –2 0 –5

Of the following inequalities, which inequality could not be the inequality that Tyler wrote?

A.

B.

C.

D.

18. Peyton makes bracelets of two kinds: those with beads and those with stones. She can make

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at most 25 bracelets in one week. Peyton makes at most 8 bracelets with beads per week, which she sells for $35 each. The bracelets with stones sell for $45 each. Peyton wants to sell at least $1,000 in bracelets this week. Use b to represent the number of bracelets with beads and s to represent the number of bracelets with stones. Which set of inequalities bounds the acceptable region for Peyton's sales?

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A.

B.

C.

D.

19. Given the inequality which of the following statements is true?

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A.The inequality is true only when

B. The inequality is true only when x = 0.

C.The inequality is true only for all real numbers greater than or equal to

D. The inequality is true only for all real numbers greater than or equal to 0.


A. The cost of x sandwiches that cost $5 each equals the cost of 3x hot dogs that cost $8 each.

B. The cost of x sandwiches that cost $5 each equals the cost of x + 8 hot dogs that cost $3 each.

C. The cost of x sandwiches that cost $5 each is $8 less than the cost of x hot dogs that cost $3 each.

D. The cost of x sandwiches that cost $5 each is $8 more than the cost of x hot dogs that cost $3 each.

21. The graph of a system of inequalities is shown.

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What are the constraints to the system?

A.

B.

C.

D.

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22. Karen sells clothes. After studying her constraints, she knows that she will make a $10 profit on each jacket, j, she sells and $6 profit on each shirt, s, she sells. Which equation or inequality should she use to show her maximum profit, P?

A. P > 10j + 6s

B. P = 10j + 6s

C. P > 6j + 10s

D. P = 6j + 10s

23. Doris needs to purchase at least 40 party decorations. The Party Palace charges $0.50 per decorative streamer and $0.25 per balloon, including tax. Which combination of streamers and balloons can Doris purchase with $12.50 at the Party Palace?





24. A company needs to sell at least 30 subscriptions, s, for every free subscription, c, they give away. Which inequality would be representative of this constraint?

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A. s ≥

30c

B. s ≥ 30 +

c

C. c ≤

30s

D. c ≤ 30 +

s

25. Enrique needs to buy hamburgers and hot dogs for a picnic. He has only $16.50 to spend and must buy at least 44 hamburgers or hot dogs. A store charges $.50 per hamburger and $0.25 per hot dog. Which of the following is a possible way Enrique might buy the hamburgers and hot dogs?





26. The sign chart below shows intervals determined by the zeros for the numerator and

denominator of

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What is the solution to

A.

B.

C.

D.

27.Ralph assembles pieces of furniture at a factory. It takes him hours to assemble a

desk. It takes him hours to assemble a chair. Ralph can work no more than 40 hours each week. During the week, he must assemble at least 10 chairs and a total of at least 12 pieces of furniture.

In the following inequalities, d represents the number of desks and c represents the number of chairs that Ralph can assemble within one week. Which system of inequalities can Ralph use to determine the

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maximum number of each item he can assemble?

/files/assess_files/7c08809e-000b-4eb9-bdef-882157ad25e8/formula_sheets/FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf


A.

B.

C.

D.

28. One acute angle of a right triangle is 36° more than twice the other angle. Which of the following systems of equations could be used to find the smaller

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angle?

A.

B.

C.

D.

29. Three friends each have different monthly payment plans for sending text messages.

Naomi pays a flat fee of $30 for an unlimited number of text messages.

Tina pays a base fee of $6.00 plus $0.10 per text message. Chris pays a base fee plus $0.05 per text message. Last month,

he paid $18.00 for 100 text messages.

Naomi researched how much she would have to pay if she switched to Tina or Chris's plan. She decided that her plan is the least expensive based on the number of text messages she uses each month. What is the minimum number of text messages Naomi must use each month for her plan to be the least expensive?

/files/assess_files/a96cc99c-9e9c-440c-88ff-66cb213510cc/formula_sheets/FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf


A. 140 text messages

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B. 241 text messages

C. 341 text messages

D. 601 text

messages

30. Alyssa has $150 to spend on new school clothes.

She wants to buy at least 2 times as many shirts as pairs of pants.

Each shirt costs $15, and each pair of pants costs $20.

What is the maximum number of pairs of pants that Alyssa can buy to meet the constraints?

A. 2

B. 3

C. 6

D. 10

31. Xian is planning a party at the skating rink. The cost for each person attending is $3.50 for skate rental and $5.00 for food. Xian cannot spend more than $300. Which inequality could

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be used to find the greatest number of people, p, that can attend?

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A.

B.

C.

D.

32. What are all values of x for which the expression is not a real number?

A.

B.

C.

D.

33. Andre needs to buy hamburgers and hot dogs for a picnic. He has only $23.00 to spend and must buy at least 78 hamburgers or hot dogs. A store charges $0.50 per

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hamburger and $0.25 per hot dog. Which of the following is a possible way Andre might buy the hamburgers and hot dogs?





34. Jenny is baking cakes and pies.

Each cake requires 1.25 cups of flour and 2 eggs. Each pie requires 1 cup of flour and 1 egg. Jenny has 12 cups of flour and 18 eggs.

Using the ingredients she has, which is a possible number of cakes and pies Jenny can make?

A. 5 cakes and 6 pies

B. 6 cakes and 5 pies

C. 7 cakes and 4 pies

D. 8 cakes and 2 pies

35. A computer company hopes to sell more than 4 times as many laptop computers as desktop computers. The company sold 10

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desktop computers last week. Which would be a viable number of laptops the company could sell to meet their goal?

A. 27

B. 36

C. 40

D. 52

36. Clyde needs to buy hamburgers and hot dogs for a picnic. He has only $27.50 to spend and must buy at least 62 hamburgers or hot dogs. A store charges $.50 per hamburger and $0.25 per hot dog. Which of the following is a possible way Clyde might buy the hamburgers and hot dogs?





37. Sarah is going to eat raisins and bananas in order to get the amount of potassium recommended each day.

She wants to eat at least 1 box of raisins and at least 2 bananas each day.

Each box of raisins has 322 mg of potassium and 129

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calories. Each banana has 361 mg of potassium and 90 calories. She needs between 2,000 and 2,500 mg of potassium

each day.

Which system below could be used to find the number of boxes of raisins, x, and bananas, y, that Sarah needs to minimize her weekly calorie intake?

A. x ≥ 1y ≥ 2 14,000 ≤ 322x + 361y ≤ 17,500 Calories = 129x + 90y

B. x ≥ 1y ≥ 2 2,000 ≤ 322x + 361y ≤ 2,500 Calories = 129x + 90y

C. x ≥ 7y ≥ 14 14,000 ≤ 322x + 361y ≤ 17,500 Calories = 129x + 90y

D. x ≥ 7y ≥ 14 2,000 ≤ 322x + 361y ≤ 2,500 Calories = 129x + 90y

38. Gabriel needs to purchase at least 30 party decorations. The Party Palace charges $0.50 per decorative streamer and $0.25 per balloon, including tax. Which combination of streamers and balloons can Gabriel purchase with $12.50 at the Party Palace?

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39. A high school band is planning a trip that will cost $180 per person. The band has a bake sale to raise money. They charge $1.50 for a bag of cookies and $8.00 for a pie. Which combination would pay for the 16 band members to go on the trip and have extra spending money?

A. 320 bags of cookies, 300 pies

B. 264 bags of cookies, 320 pies

C. 192 bags of cookies, 324 pies

D. 64 bags of cookies, 348 pies

40. Two customers each bought sets of tables and chairs from a furniture store offering a single price for chairs and a single price for tables. The amount paid by each customer is represented by the following inequalities, where c is the price of a single chair and t is the price of a single table.

Which could be the prices for a single chair and a single table?

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A. Chair: $20, Table: $40

B. Chair: $22, Table: $60

C. Chair: $25, Table: $40

D. Chair: $30, Table: $60

41. A club will create t-shirts for a fundraiser. The club members need to compare the cost of creating the t-shirts between two companies. Company A charges $30 for setup, plus $5 per t-shirt. Company B charges $15 for setup, plus $7 per t-shirt.

Which option below best interprets the results from the graphic solution of

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these paired equations?

A. For orders less than or equal to 7 shirts, the cost using Company A is less.

B. For orders less than or equal to 8 shirts, the cost using Company A is less.

C. For orders less than or equal to 7 shirts, the cost using Company B is less.

D. For orders less than or equal to 8 shirts, the cost using Company B is less.

42. A store sells two types of speakers, A and B; x represents the number of type A speakers sold daily, and y represents the number of type B speakers sold daily. The system of inequalities below represents the possible values of x and y for this situation.

If the store’s daily profit is represented by the function what is the maximum daily profit for the store?

/files/assess_files/f92b0115-c49c-483e-9f83-5ed170be7e75/formula_sheets/FL-

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IBTP_Math_Reference_Sheet_Grade_9-12.pdf


A. $700

B. $740

C. $760

D. $800

43. Steve and Emerik collected donations of $1 bills and $5 bills for the upcoming fundraising walk at their school. Steve counted the money and then told Emerik the following.

There is at least one of each bill. There are fewer than 60 bills all together and less than $100 total.

If x represents the number of dollar bills and y represents the number of $5 bills, which system of inequalities could Emerik use to determine the possible numbers of each bill?

A.

B.

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C.

D.

44. Jill bakes banana bread and nut bread for a bake sale.

Banana bread uses 2 eggs and half a pound of flour. Nut bread uses 1 egg and 1 pound of flour. Jill has 8 eggs and 5 pounds of flour to use. She makes a profit of $3 for each loaf of banana bread and

$2 for each loaf of nut bread.

How many loaves of banana bread should Jill bake to maximize her profit?

A. 0

B. 2

C. 4

D. 5

45. A factory produces x packs of pencils and y packs of pens each day.

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The factory can produce no more than a total of 50 packs of pens and pencils each day.

At least 10 packs of pencils are produced each day. At least 20 packs of pens are produced each day. The company makes $0.25 on a pack of pencils and $0.50

on a pack of pens.

What are the vertices of the feasible region for the system of inequalities that models the constraints?

A. (10, 20), (10, 40), (30, 20)

B. (20, 10), (20, 30), (40, 10)

C. (15, 40), (30, 40), (30, 50)

D. (20, 20), (25, 15), (25, 40)

46. A bakery sells pies and cakes.

The bakery expects to sell at least 50 pies and 35 cakes per day.

The bakery is not capable of making more than 125 pies and 75 cakes each day.

A total of at least 100 desserts must be delivered each day to satisfy delivery contracts.

Which graph shows the region containing the number of pies, x, and the number of cakes, y, that should be made each day?

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A.

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B.

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C.

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D.

47. Tina has $50 to spend at the carnival.

Each game costs $2 to play. Each ride costs $4. Tina wants to play at least 6 games and ride on at least 3

rides.

What is the maximum number of games Tina can play, if she rides the most rides possible?

A. 6

games

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B. 7

games

C. 8

games

D. 9

games

48. Annie is filling two buckets. The depth of the water in the buckets is a function of time in minutes and is modeled by the two lines shown in the graph below.

From the graph, Annie determines that the two buckets will reach the same depth at 5.5 minutes. Which of the following best explains the precision of Annie’s solution?

A. The solution is precise because the two lines appear to intersect at 5.5 on the

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horizontal axis.

B. The solution is precise because an algebraic solution yields the same solution for time, t =5.5.

C. The solution is not precise because and.

D. The solution is not precise because and

49. Laurel needs to purchase at least 40 party decorations. The Party Palace charges $0.50 per decorative streamer and $0.25 per balloon, including tax. Which combination of streamers and balloons can Laurel purchase with $16.00 at the Party Palace?





50. Gabriela and her mother sell sweatshirts for $25 and tie dyed t-shirts for $10.50. They are positive more than 10 t-shirts and at least 2 sweatshirts will be sold this weekend. If they want to make at least $400, which system could be used to determine the possible numbers of sweatshirts (s) and t-shirts (t) they would need to sell?

A.

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B.

C.

D.

51. Cody is considering going sailing during the summer. He is comparing the prices of two companies that rent the necessary equipment. Water Adventures charges $35 per hour to rent a sailboat plus a $14 fee for a wetsuit. Boat World charges $22 per hour to rent a sailboat plus a $40 fee for a wetsuit. Cody wants to determine the number of hours that Water Adventures will cost less than Boat World. Let x represent the number of hours Cody will spend sailing. Which inequality correctly compares the total costs for sailing at the two companies?

/files/assess_files/12873326-a2d3-45df-a4ce-59e98885e3b6/formula_sheets/FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf


A.

B.

C.

D.

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52. A factory has 161 workers. There are 92 more males than females. Let x represent the number of males and let y represent the number of females. Which system of equations represents this situation?

A.

B.

C.

D.

53. Karen is making bird houses, x, and dog houses, y, to earn money. She found that her feasible region intersected at the points (9, 20), (0, 16), and (11, 0). She knows that she will lose $1 on each bird house, but will make $5 on each dog house that she sells. How many dog houses will Karen need to sell to maximize her profit?

A. 91

B. 80

C. 20

D. 16

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54. The students of Lincoln High School are raising money to support the sports teams. A local organization donated boxes of popcorn and candy for the students to sell. The freshmen are selling boxes of popcorn for $2 each, and the sophomores are selling boxes of candy for $4 each. The students' target is to raise more than $800. The sophomores expect to sell at most 100 boxes of candy. Let x represent the number of boxes of popcorn sold and y represent the number of boxes of candy sold. Which system of inequalities models the given situation?

/files/assess_files/0671a7f1-0881-42f8-905c-948e6003637a/formula_sheets/FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf


A.

B.

C.

D.

55. Mai Ly’s bag contains red and blue beads. The number of red beads in the bag (r) is at

least the number of blue beads in the bag (b). There are at most 400 beads in the bag. Which system of inequalities could be used to determine the number of red beads in Mai Ly’s bag?

A.

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B.

C.

D.

56. Which of the following situations can be modeled by the inequality below?

A. The 7.5% sales tax on an item is $0.07 greater than the cost of the item without sales tax.

B. The 7.5% sales tax on an item is greater than the cost of the item including 7% sales tax.

C. The cost of an item including 7.5% sales tax is $0.07 greater than the cost of the item without sales tax.

D. The cost of an item including 7.5% sales tax is greater than the cost of the item

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including 7% sales tax.

57. A system of inequalities is shown below.

3

x – y

> –

1

x –

2

y

> 4

Which is a solution to the system?

A. (–2, –4)

B. (–2, –1)

C. (1, 2)

D. (2, –4)

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58. A wholesale distributor of packaged nuts sells two different mixes of peanuts and cashews, mix A and mix B. Each package of mix A nuts contains 8 ounces (oz.) of peanuts and 4 oz. of cashews. Each package of mix B nuts contains 6 oz. of peanuts and 6 oz. of cashews. Let x represent the number of packages of mix A nuts and let y represent the number of packages of mix B nuts. No more than 120 oz. of peanuts and no more than 96 oz. of cashews can be used each day. Which graph represents the numbers of packages of mix A and mix B that can be produced?

/files/assess_files/3b5cc70c-e84d-4787-ab01-a99dee7ec124/formula_sheets/FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf


A.

B.

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C.

D.

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59. Greg makes chairs and tables.

Each chair takes him 4 days to make. Each table takes him 6 days to make. Greg works no more than 26 days in a month. Greg makes at least 2 tables a month.

What is the maximum number of chairs Greg can make in one month?

A. 6

B. 5

C. 4

D. 3

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60. Cell phone companies try to sell at least 4 smartphones for every 1 non-smartphone. If x is the number of smartphones and y is the number of non-smartphones, which ordered pair meets the constraint?

A. (11, 57)

B. (47, 25)

C. (63, 15)

D. (97, 25)

61. A company produces packs of pencils and pens.

The company produces at least 100 packs of pens each day but no more than 240.

The company produces at least 70 packs of pencils each day but no more than 170.

A total of less than 300 packs of pens and pencils are produced each day. Each pack of pens makes a profit of $1.25. Each pack of pencils makes a profit of $0.75.

What is the maximum profit the company can make each day?

A. $338.75

B. $344.25

C. $352.50

D. $427.50

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62. Susan wants to make cupcakes and cookies to sell at the school bake sale.

It takes her 30 minutes to make a dozen cookies and 1 hour to make a dozen cupcakes.

It costs her $3 to buy supplies for each dozen cookies and $4 to buy supplies for each dozen cupcakes.

She has 14 hours available to cook and has $50 to spend on supplies.

She will make at least 1 dozen cookies and 1 dozen cupcakes.

Which system of inequalities models these constraints?

A. 0.5x + y ≤ 50 3x + 4y ≤ 14x ≥ 1y ≥ 1

B. 0.5x + y ≤ 50 4x + 3y ≤ 14x ≥ 1y ≥ 1

C. 0.5x + y ≤ 14 3x + 4y ≤ 50x ≥ 1y ≥ 1

D. 0.5x + y ≤ 14 4x + 3y ≤ 50x ≥ 1y ≥ 1

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63. Anna had $5000, which she invested in two different banks. She deposited x amount of money in bank A, which paid 3.5% simple interest annually. She deposited y amount of money in bank B, which paid 1.2% simple interest annually. The total interest Anna earned over a 6-year period was $774. Which system of equations represents the given situation?

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A.

B.

C.

D.

64. Travelz is organizing a three-day city tour and is charging $150 for each adult and $75 for each child. There are twice as many children on the trip as there are adults. The total amount collected for the number of adults, a, and the number of children, c, that are taking the tour is $5250. Which of these equations can be used to find the total number of adults and children on the tour?

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A.

B.

C.

D.

65. Rita deposited less than $1,000 into two accounts. One account paid 2.5% and the other account paid 2% annual interest. After 1 year, she earned at least $23 in interest from the two combined accounts. If x represents the amount of money Rita deposited at 2.5% and y represents the amount of money she deposited at 2%, which system of inequalities can be used to find the values of x and y?

A.

B.

C.

D.

66. Graham has enough fencing to enclose a rectangular garden with a perimeter of 140 feet. If the width of his garden is 20 feet less than the length, what is the

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width of the garden?

A. 20 feet

B. 25 feet

C. 40 feet

D. 45 feet

67. The length, x, of a rectangular garden is 4 times the width, y. Cody estimates that the perimeter of the garden is 70 meters. Which system of equations models the dimensions of the garden?

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A.

B.

C.

D.

68. Eli created the graph shown below of a system of two equations. From the graph, Eli determined that the system has no solution.

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Which choice best explains whether or not Eli is correct?

A. Eli is correct. The two lines appear to be parallel, so there is no solution to both equations.

B. Eli is correct. The two lines have the same slope, so there is no solution to both equations.

C. Eli is incorrect. The two lines appear to be parallel, so there are infinitely many solutions to the equations.

D. Eli is incorrect. The two lines have different slopes, so there is a solution that does not appear in the graph.

69.Which statement is true for the inequality

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A. The inequality is never true.

B. The inequality is true for all values of x.

C. The inequality is only true for values of x between and 1, inclusive.

D. The inequality is not true for all values of x between 0 and 1, inclusive.

70. The volume of a sphere, S, is at least one-third the volume of a cone, C. The volume of the cone is no more than 150 cubic centimeters. Which system of inequalities below represents this problem?

A.

B.

C.

D.

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71. A system of inequalities is shown below.

Which point is a viable solution to the system?

A. (1, –2)

B. (4, –3)

C. (6, 2)

D. (8, –4)

72. A high school is hosting a basketball tournament. Their goal is to raise at least $1,500.00. Students can buy tickets for $3.00 and non-students for $5.00. The seating capacity for the gym is 400 people. Which could represent the number of each type of ticket sold to meet the high school’s goal and not exceed the capacity of the gym?

A. 100 student, 200 non-student

B. 125 student, 175 non-student

C. 150 student, 350 non-student

D. 170 student, 229 non-student

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73. Jerry works for a cable television company. He must sell at least 10 television packages over the next week. Customers have two packages to pick from, Package X and Package Y.

Jerry has to sell at least 2 of each package. He can sell at most 12 of Package X. He makes $30 for each Package X he sells. He can sell no more than 17 of Package Y. He makes $25 for each Package Y he sells.

Which inequality is a constraint for Jerry’s sales?

A. x ≥ 12

B. y ≥ 2

C. x + y > 10

D. 30x + 25y ≥ 55

74. A farmer has 12 acres of land. He plans to plant w acres of wheat and b acres of barley on his land. If he plans to plant wheat in no more than 3 acres of land, which system of inequalities represents the possible values for b and w?

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A.

B.

C.

D.

75. Duane went to the store to buy hot dogs and buns for a cookout.

He needs at least 70 of each item. Each package of hot dogs contains 10 hot dogs and costs

$4.50. Each package of buns contains 8 buns and costs $1.75. Duane does not want to have any leftover buns.

What is the minimum total price Duane will pay for the hot dogs and buns?

A. $43.75

B. $45.50

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C. $47.25

D. $51.75

76. Peggy is saving her money. She has a total of $70 in quarters and dollar bills. If the number of dollar bills Peggy has is three times the number of quarters, which equations will help her determine the number of quarters,x, and dollar bills, y, she has?

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A.

B.

C.

D.

77. The graph of a system of linear inequalities is shown.

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What are the constraints to the system of linear equations?

A.

B.

C.

D.

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78. A factory produces cars and trucks to sell.

The factory can produce no more than 60 vehicles per day.

The factory produces at least 25 cars each day. The factory produces at least 15 trucks each day. The factory makes $2,000 profit on each car. The factory makes $4,000 profit on each truck.

How many of each type of vehicle should the company make to maximize profit?

A. 25 cars and 35 trucks

B. 30 cars and 30 trucks

C. 35 cars and 25 trucks

D. 45 cars and 15 trucks


A. The 8% sales tax on an item equals the cost of the item less $1.25.

B. The 8% sales tax on an item equals the cost of the item plus $1.25.

C. The cost of an item including 8% sales tax is $1.25 less than the cost of the item

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without sales tax.

D. The cost of an item including 8% sales tax is $1.25 greater than the cost of the item without sales tax.

80. A furniture store is offering discounts of 30% on a blue couch and 60% on a white couch. The original cost of the couches exceeded $1,260. The total discounted cost of the couches exceeds $630. If b represents the original cost of the blue couch and w represents the original cost of the white couch, which system of inequalities can be used to find the possible values of b and w?

A.

B.

C.

D.

81. Farrah needs to purchase at least 45 party decorations. The Party Palace charges $0.50 per decorative streamer and $0.25 per balloon, including tax. Which combination of streamers and balloons can Farrah purchase with $16.00 at the Party Palace?




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82. Marlene needs to purchase at least 50 party decorations. The Party Palace charges $0.50 per decorative streamer and $0.25 per balloon, including tax. Which combination of streamers and balloons can Marlene purchase with $19.50 at the Party Palace?





83. If the sum of x and y is 90 and y is 6 more than four times x, which of the following systems of equations could be used to solve for x and y?

A.

B.

C.

D.

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84. This summer Paige’s town will be hosting a series of 9 concerts. There are two types of seats at the concerts, which are priced at $29.50 and $43.00. Paige would like to attend at least 5 concerts and spend no more than $200. If x and y represent the number of tickets Paige purchased for the 2 types of seats, which system of inequalities could Paige use to model this situation?

A.

B.

C.

D.

85. Jerry planted a pine tree that was 5 feet tall and a maple tree that was 10 feet tall. The pine tree grew 3 feet taller per year and the maple tree grew 2 feet taller per year. Which comparison is described by the inequality below?

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A. After x years, the pine tree is taller than the maple tree.

B. After x years, the pine tree is at least as tall as the maple tree.

C. After 3x years, the pine tree is taller than the maple tree was after 2x years.

D. After 3x years, the pine tree is at least as tall as the maple tree was after 2x years.

86. Fateen sells handbags and wallets. Handbags sell for $12 and wallets for $4. Fateen wants to sell at least 60 items this month for a total of at least $400. Which set of inequalities could be used to determine the number of handbags (h) and wallets (w) Fateen should sell?

A.

B.

C.

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D.

87. A delivery truck can transport packages weighing at most 3,800 pounds (lbs) and with a

volume of no more than 400 cubic feet The truck transports only two sizes of packages: a small package weighing 30 lbs with a volume of 4 and a large package weighing 65 lbs with a volume of 9 Let x represent the number of small packages and y represent the number of large packages. Which system of inequalities describes the possible numbers of packages the truck can transport at one time?

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A.

B.

C.

D.

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88. The Student Council is having a talent show.

They plan to sell no more than 500 student tickets and no more than 300 general admission tickets.

It costs $0.50 per ticket to advertise the show to the students and $1 per ticket to advertise the show to the general public.

The advertising budget is, at most, $400 for the show. Student Council makes $6 profit for a student ticket and $9

profit for a general admission ticket.

What is the maximum profit that the Student Council can expect from the show?

A. $4,350

B. $3,900

C. $3,000

D. $2,750

89. Marisol needs to purchase at least 55 party decorations. The Party Palace charges $0.50 per decorative streamer and $0.25 per balloon, including tax. Which combination of streamers and balloons can Marisol purchase with $19.00 at the Party Palace?




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90. A pottery shop sells plates and bowls.

The shop expects to sell, at least, 10 plates and 15 bowls each day.

The shop expects to sell, at most, 50 total pieces each day.

Each plate sells for $14 and each bowl sells for $8.

How many bowls does the shop sell if they made the maximum daily income?

A. 10

B. 15

C. 35

D. 40

91. Michael was given the constraints below.

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What is the maximum value of W?

A. 10

B. 8

C. 6

D. 4

92. Nathan has a savings account that he deposits $4.00 into each week. He has a checking account with an initial balance of $60.00 that he uses to make a regular $6.00 weekly payment. Nathan creates a graph of the balances for these two accounts as a function of time in weeks.

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From the graph, Nathan concludes that the balance in the accounts is the same at 6 weeks. Which option best supports Nathan’s conclusion?

A. The two lines in the graph appear to intersect near (6, 25).

B. Substituting t = 6 into both equations for b gives the same value: b = 25.

C. Equating the two equations for b and solving for t gives the solution t = 6.

D. The point of intersection falls on both lines, and therefore solves both equations.

93. Paul sells chocolate chip cookies and peanut butter cookies.

Baking a batch of chocolate chip cookies takes 1.75 cups of flour and 2

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eggs. Baking a batch of peanut butter cookies takes 1.25 cups of flour and 1 egg. Paul has 10 cups of flour and 12 eggs. He makes $4 profit per batch of chocolate chip cookies. He makes $2 profit per batch of peanut butter cookies.

How many batches of peanut butter cookies should Paul make to maximize his profit?

A. 1

B. 2

C. 5

D. 8

94. A dance department is planning a holiday show. The department needs to raise at least $450 in order to cover the cost of costumes and decorations. Tickets will be sold at $5 for adults and $3 for students. Let a represent the number of adult tickets and s represent the number of student tickets. Which inequality should be used to represent the number of tickets that must be sold in order to raise the amount of money needed for the show?

/files/assess_files/379ad0ef-00b7-4cb0-8649-aad6b5e0e96b/formula_sheets/FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf


A.

B.

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C.

D.

95. Eugenia needs to buy hamburgers and hot dogs for a picnic. She has only $28.00 to spend and must buy at least 80 hamburgers or hot dogs. A store charges $.50 per hamburger and $0.25 per hot dog. Which of the following is a possible way Eugenia might buy the hamburgers and hot dogs?





96. Trevor is making two types of bracelets.

Each Type P bracelet needs 12 inches of leather and 3 inches of string.

Each Type Q bracelet needs 4 inches of leather and 18 inches of string.

Trevor has 5 yards of leather and 6 yards of string. x equals the number of Type P bracelets Trevor makes. y equals the number of Type Q bracelets Trevor makes.

Which system of equations models the constraints on the number of bracelets Trevor can make?

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A. 12x + 4y ≤ 180 3x + 18y ≤ 216x ≥ 0y ≥ 0

B. 12x + 3y ≤ 180 4x + 18y ≤ 216x ≥ 0y ≥ 0

C. 12x + 4y ≤ 5 3x + 18y ≤ 6x ≥ 0y ≥ 0

D. 12x + 3y ≤ 5 4x + 18y ≤ 6x ≥ 0y ≥ 0

97. Evan has a job selling magazine and newspaper subscriptions. He earns $23 for each magazine subscription and $54 for each newspaper subscription that he sells. His goal is to make more than $642 per week. He expects to sell at least 10 subscriptions per week. If m represents the number of magazine subscriptions sold and n represents the number of newspaper subscriptions sold, which system of inequalities models the given situation?

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A.

B.

C.

D.

98. Based on the values in the table, which inequality would have all of these values in its solution set?

x y

0 42 5–4 8–2 610 –1

A.

B.

C.

D.

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99. Carlos and Thomas are each buying motor scooters and bicycles. Carlos buys 6 scooters and 3 bicycles for $4515. Thomas buys 5 scooters and 4 bicycles for $3995. Which system of equations can be used to determine the cost of one scooter, where s represents the number of of scooters and b represents the number of bicycles?

/files/assess_files/1b44faed-7655-49e3-a544-4852298aad84/formula_sheets/FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf


A.

B.

C.

D.

100.

The Medina family bought trees and bushes for their backyard staying within their $700 budget. If trees are priced at $49 and bushes at $19, which inequality describes this situation?

x = number of trees

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y = number of bushes

A.

B.

C.

D.

101.

An electronics store sells monitors and scanners. The store estimates that at least 30 monitors and scanners will be sold each month and that the number of monitors sold will be at least 20% more than the number of scanners. The monitors cost the store $1000 each and are sold for $1050. The scanners cost $300 each and are sold for $350. If the store can spend only $30,000 on both monitors and scanners, what is the store’s maximum monthly profit given the constraints listed?

/files/assess_files/0617d4d9-02d0-41a4-9242-0e7bbe567d0d/formula_sheets/FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf


A. The store can earn a maximum profit of $1500.

B. The store can earn a maximum profit of $2200.

C. The store can earn a maximum profit of $30,000.

D. The store can earn a maximum profit of $32,200.

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102.

Which of the following situations can be modeled by the inequality below?

A. Damon drives at 60 miles per hour for a certain amount of time. Lily drives at

50 miles per hour for 3 hours more than Damon. Damon drives farther than Lily.

B. Damon drives at 60 miles per hour for a certain amount of time. Lily drives at

50 miles per hour for 3 hours more than Damon. Lily drives farther than Damon.

C. Damon drives at 50 miles per hour for a certain amount of time. Lily drives at

60 miles per hour for 3 hours more than Damon. Damon drives farther than Lily.

D. Damon drives at 50 miles per hour for a certain amount of time. Lily drives at

60 miles per hour for 3 hours more than Damon. Lily drives farther than Damon.

103.

The Math Club has a budget of $100 for a pizza party. The club can get large pizzas, x, for $12 and cases of soda, y, for $5.50. The club would like to buy at least 6 large pizzas and at least 4 cases of soda. Which system models the situation?

A.

B.

C.

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D.

104.

An amusement park charges $17 for each adult ticket and $6 for each child ticket. One day, the park earned $3,640 in ticket sales. Let x represent the number of adult tickets sold. Let y represent the number of child tickets sold. If 400 tickets were sold on this day, which system of equations can be used to find the number of each type of ticket sold?

/files/assess_files/bb0231a0-9c72-483f-83ff-7e408784cc77/formula_sheets/FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf


A.

B.

C.

D.

105.

A system of inequalities is shown below.

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Which point is a viable solution to the system?

A. (4, –1)

B. (3, 2)

C. (5, –2)

D. (7, 0)

106.

A bakery sells cakes, c, and donuts, d. The bakery makes a profit of $6 for each cake it sells and a profit of 45 cents for each donut it sells. Which equation or inequality should the bakery use to show its maximum profit?

A. P > 6c + 0.45d

B. P = 6c + 0.45d

C. P > 6c +

45d

D. P = 6c +

45d

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107.

Which of the following situations can be modeled by the equation below?

A. Five times the width of a rectangle is 9 inches more than 3 times the width.

B. Three times the width of a rectangle is 9 inches more than 5 times the width.

C. Five times the width of a rectangle equals 3 times the sum of the width and 9 inches.

D. Three times the width of a rectangle equals 5 times the sum of the width and 9 inches.

108.

Dr. Smith’s office is open 8 hours a day. The doctor allows 25 minutes for office visits and 50 minutes for procedures. The doctor can perform up to 5 procedures per day. Let x represent the number of office visits and y the number of procedures. Which system of inequalities models this scenario?

A. 0 ≤ x ≤ 5

0 ≤ y 25x + 50y ≤ 480

B. 0 ≤ x ≤ 19

0 ≤ y ≤ 5 25x + 50y ≤ 480

C. 0 ≤ x

0 ≤ y ≤ 5 25x + 50y ≤ 8

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D. 0 ≤ x ≤ 5

0 ≤ y ≤ 19 25x + 50y ≤ 8

109.

Charlotte makes bracelets.

A small bracelet costs $0.50 to make and takes a half hour to create.

A large bracelet costs $1.50 to make and takes an hour to create.

Charlotte has only $20 for supplies and 10 hours to work on bracelets each week.

Which is a possible number of small and large bracelets that Charlotte can make each week?

A. 2 small, 13 large

B. 6 small, 7 large

C. 8 small, 12 large

D. 14 small, 6 large

110.

The Thompson family went to a baseball game. Mrs. Thompson has $30 to buy hamburgers and drinks for herself and 4 family members.

Each hamburger costs $4.00 and each drink costs $2.50. Each person will get a drink.

What is the maximum number of hamburgers that Mrs.

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Thompson can buy?

A. 4

B. 5

C. 6

D. 7

111.

A senior class of 30 students needs to raise $19,000 to pay for their end-of-year trip. They are hosting a dinner at a banquet hall that can seat up to 2,500 people. A child’s dinner will cost $8 and an adult’s dinner will cost $12. Which solution would notbe viable in order to meet or exceed their goal?

A. 500 children, 2,000 adults

B. 750 children, 1,600 adults

C. 1,000 children, 900 adults

D. 1,250 children, 800 adults

112.

The measures of the acute angles of the right triangle below are represented by x and y. In this triangle, y is 15 less than twice x.

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Which system of equations could be used to solve for x and y?

A.

B.

C.

D.

113.

Cecil is buying almonds and cashews.

A bag of almonds costs $7.00 and a bag of cashews costs $9.00.

Cecil has $60 to spend on the nuts. Cecil wants to purchase at least 2 bags of almonds. Cecil does not want the cost of the cashews to exceed the

cost of the almonds.

What is the maximum number of bags of cashews that Cecil can buy?

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A. 2

B. 3

C. 4

D. 5

114.

A coffee shop is having a clearance sale for two types of coffee beans, arabica and robusta. The coffee shop is charging $3 per pound for arabica beans and $4 per pound for robusta beans. On a given day, a total of 55 pounds of coffee beans was sold, and $195 was the total value of the sales. Which statement accurately compares the sales of the two types of coffee beans for this day?

/files/assess_files/ed303de8-9ec3-4810-aaea-bf35d3957289/formula_sheets/FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf


A. The coffee shop took in $5 more selling arabica beans.

B. The coffee shop took in $5 more selling robusta beans.

C. The coffee shop took in $45 more selling arabica beans.

D. The coffee shop took in $45 more selling robusta beans.

115.

Allison’s cupcake and cookie budget for her party is $105. She would like to have at least 40 cupcakes and cookies combined, and would like to have at most 5 more cupcakes than cookies. If cupcakes sell for $2.50 and cookies for $1.50, which system

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of inequalities could help Allison determine possible numbers of cupcakes (a) and cookies (b) that she should buy?

A.

B.

C.

D.

116.

One solution for the equation has an x-value that is five times its y-value. What is that solution?

A. (3, 15)

B. (4, 8)

C. (15, 3)

D. (20, 40)

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117.

A baseball team hosts an exhibition game in order to raise at least $5,000 for new equipment. Regular stadium seats sell for $5 each, but each of the 400 premium seats sells for $10.

The coach draws up a feasible region in the coordinate plane, where x represents the number of premium seats the game sells, and y represents the number of regular seats the game sells. Which of the following inequalities is NOT a boundary condition for the feasible region?

/files/assess_files/a47d5dd2-1951-41c3-a177-9ec428d88066/formula_sheets/FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf


A.

B.

C.

D.

118.

A certain roller coaster ride at a theme park can hold up to 50 people, both children and adults. On a particular day, due to mechanical issues, 4 seats cannot be used. On that day, which combination would be a viable solution?

A. 24 children, 26 adults

B. 28 children, 20 adults

C. 30 children, 11 adults

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D. 32 children, 15 adults

119.

Nicki needs to purchase at least 65 party decorations. The Party Palace charges $0.50 per decorative streamer and $0.25 per balloon, including tax. Which combination of streamers and balloons can Nicki purchase with $20.00 at the Party Palace?





120.

Liana needs to purchase at least 50 party decorations. The Party Palace charges $0.50 per decorative streamer and $0.25 per balloon, including tax. Which combination of streamers and balloons can Liana purchase with $15.00 at the Party Palace?





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121.

At the grocery store, halibut costs $20 per pound and salmon costs $17 per pound. Which of the following situations can be modeled by the equation below?

A. The cost of x pounds of salmon is $5 less than the cost of x pounds of halibut.

B. The cost of x pounds of halibut is $5 less than the cost of x pounds of salmon.

C. The cost of x pounds of salmon is the same as the cost of x – 5 pounds of halibut.

D. The cost of x pounds of halibut is the same as the cost of x – 5 pounds of salmon.

122.

Marco has two summer jobs: tutoring, x, and working as a lifeguard, y.

He would like to tutor for at least 10 hours per week, but no more than 30 hours per week.

He also must work as a lifeguard at least 15 hours per week, but no more than 25 hours per week.

He can spend at most 40 hours per week total working both jobs.

When this information is graphed, it forms a figure showing his options for working either job that meet his constraints. What is the shape of the figure?

A. parallelogra

m

B. rectangl

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e

C. trapezoi

d

D. triangl

e

123.

Serafina needs to purchase at least 60 party decorations. The Party Palace charges $0.50 per decorative streamer and $0.25 per balloon, including tax. Which combination of streamers and balloons can Serafina purchase with $20.00 at the Party Palace?





124.

A school is collecting canned food as a service project. There are 30 classes participating in the project. The goal is to collect more than 1,000 canned food items. If each class collects the same number of cans, what is the least number of cans each class must collect to meet the goal?

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A. 30

B. 33

C. 34

D. 40

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